Multiplication By Patterns - 2

Algebra Level 1

$\large{\begin{array} { r c l } 98 ^2 & = & 9604 \\ 998^2 & = & 996004 \\ 9998^2 & = & 99960004 \\ \end{array}}$

What is $99998^2$ ?

1 solution

Nihar Mahajan
Mar 10, 2016

Note that every 99999....9998 can be expressed in the form $10^n-2$ for some integer $n>1$ . Let's see what happens when we square it:

$(10^n-2)^2 = 10^{2n} - 4\times 10^n + 4 = 10^n(10^n-4)+4$

Hence the general pattern for $n$ number of 9's is given by $10^n(10^n-4)+4$ and for this question , put $n=5$ :)

Yes! That's the explanation for the pattern :)

Chung Kevin - 5 years, 3 months ago

Thanks! Your questions are easy but quite interesting!

Nihar Mahajan - 5 years, 3 months ago